In audio signal output devices (for example, CD (Compact Disc) players or AV (Audio Visual) amplifiers), digital audio data is filtered by digital filters to be oversampled (interpolated) before being D/A (Digital-to-Analog) converted, and then are filtered by low-pass filters (LPFs) having high cut-off frequencies. As a result, any influence from the LPFs on amplitudes and phase characteristics of D/A-converted analog audio signals is reduced, thus improving sound quality.
In general, for cases in which analog audio signals are A/D (Analog-to-Digital) converted, in order that only frequencies equal to or lower than ½ of a sampling frequency “fs” be included, the analog audio signal is filtered by an aliasing filter. For instance, with a compact disc (CD), the sampling frequency “fs” thereof is 44.1 kHz. As a consequence, such digital audio data is recorded on a compact disc, the digital audio data being produced by A/D-converting analog audio signals for which the frequency range equal to or higher than 22.05 kHz has been eliminated by the aliasing filter.
In other words, although actual music signals include frequency components equal to or higher than an audible range (for example, 20 kHz), high-range components (range exceeding ½ of sampling frequency “fs”) are removed by the aliasing filter. As a consequence, some users may not be satisfied with the sound of compact discs in which high-range components are not reproduced as compared with the sound reproduced by conventional analog systems.
Under the circumstances, a method of adding high-range components was developed which carries out oversampling processing (so-called “zero-order interpolation”) by using digital filters (interpolation filters) with respect to digital audio data read out from CDs and the like (refer to, for example, JP 09-23127 A). In addition, a method has been developed involving producing higher harmonic signals and dither signals from digital audio data using non-linear processing circuits, and adding the higher harmonic signals and the dither signals to the digital audio data in response to the high-range spectral intensity of the digital audio data (refer to, for example, JP 2002-366178 A).
Further, in cases in which high-range components are added by way of zero-order interpolation using a digital filter, smoothing degrees of the obtained signal waveforms may be slightly short. As a consequence, in order to reproduce sound having higher sound quality and higher fidelity, an oversampling method is known involving carrying out oversampling processing by employing spline interpolation or Lagrange interpolation, which couples sampling points to each other in a smooth manner, instead of employing zero-order interpolation.
However, since the sampling points in the vicinity of the high range (e.g., frequency equal to ½ of sampling frequency “fs”) are intricately changed, reproducibility with fidelity in the vicinity of the high range can rarely be achieved using the oversampling method with employment of spline interpolation or Lagrange interpolation. In other words, it is difficult to obtain faithful reproductions of waveforms of original analog audio signals as waveforms of analog audio signals after being D/A-converted. Thus, distortions may readily occur.
Referring now to FIGS. 14 and 15, the technical points will be explained. In each of FIGS. 14 and 15, an abscissa axis indicates time and an ordinate axis shows amplitude. The solid line represents the waveform of an analog signal before being A/D-converted (namely, original analog signal). The broken line shows the waveform of an analog signal obtained by D/A-converting a digital signal oversampled by way of Lagrange interpolation. Symbol “o” shows a sampling point for cases in which the analog signal is sampled at a frequency “fs”. Further, FIG. 14 represents signal waveforms in a high range (frequency near fs/2). FIG. 15 shows signal waveforms in middle and low ranges (frequency <<fs/2).
As shown in FIG. 15, the waveform represented by a solid line is substantially coincident with the waveform indicated by a broken line in the middle and low ranges. On the other hand, as shown in FIG. 14, in the higher range, the waveform represented by a solid line is largely shifted from the waveform indicated by a broken line, and thus, distortion occurs. In the high range, since the total number of sampling points with respect to 1 time period of the waveforms becomes small, the original waveform can rarely be reproduced in fidelity. When Lagrange interpolation is employed, any influence from aliasing noise is readily given, causing distortions to readily occur. As described above, in the case in which oversampling processing by way of spline interpolation or Lagrange interpolation which couples the sampling points to each other in a smooth manner is employed, problems arise in that the reproducibility with a fidelity near the high range (fs/2) can rarely be obtained, and distortion may easily occur.